Hugs to you and your DS. I remember being poor at sports in school and feeling miserable about it. And now I can see my own kids struggling with the same thing - it's hard.
My own DS7 also has developmental coordination disorder (blackcat mentioned it - and I'm in agreement with what she said above). In school they've been pulling him out of class with a couple of other kids to do 'body break' exercises - they work on core strength and balance. At first he didn't want to but by the end of school he was enjoying them.
He's also just now started to get into swimming - he also really struggled with putting his head in the water - but just recently he decided to do it and worked at it until he got used to it. Now he asks to go swimming every day! Unfortunately, I can't tell you any tricks to make that happen - no swim instructors were able to persuade him, he just decided and that was it.
One other thing I thought I'd mention - my DD10 doesn't have DCD but she is very sedentary by nature. It is hard to even convince her to go for a walk with me. We recently gave geo-caching a try, and I think the game aspect of it was appealing. She quite happily went on a long hike with me to find a cache, when normally it would be like pulling teeth. One caveat - my DCD DS does not really enjoy hiking as he tends to trip on rocks and fall down a lot. He's a bit better now - but something to keep in mind with kids with balance and coordination issues. Don't know if geo-caching is a thing in Europe, but in Canada there are lots of urban caches as well as ones in natural areas.